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Equation 1 · Part 5 · God Plays Dice, and Evolution Loads Them

=

S=∣E(a,b)−E(a,b′)+E(a′,b)+E(a′,b′)∣≤2S = \left| E(a,b) - E(a,b') + E(a',b) + E(a',b') \right| \le 2
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

EPR’s paper stayed a philosophical argument until 1964, when John Bell showed it could be turned into an experiment [ 3 ] . Bell proved that any theory obeying both locality — no faster-than-light influence — and realism, in the sense of outcomes fixed by pre-existing local properties, must satisfy a statistical bound. For a simple two-setting test, S=∣E(a,b)−E(a,b′)+E(a′,b)+E(a′,b′)∣≤2S = \left| E(a,b) - E(a,b') + E(a',b) + E(a',b') \right| \le 2. holds for any local realist theory, while quantum mechanics allows S up to 22\sqrt{2} ≈\approx 2.83 . Early experimental violations left the detection loophole (too many unmeasured particles to rule out a biased subsample) and the locality loophole (stations not separated fast and far enough to exclude a hidden signal) open to…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.